Abstract

We present an $O(\lg \lg n)$‐competitive online binary search tree, improving upon the best previous (trivial) competitive ratio of $O(\lg n)$. This is the first major progress on Sleator and Tarjan’s dynamic optimality conjecture of 1985 that $O(1)$‐competitive binary search trees exist.

MSC codes

  1. 68P05
  2. G8P10

Keywords

  1. binary search trees
  2. splay trees
  3. competitiveness

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 240 - 251
ISSN (online): 1095-7111

History

Submitted: 23 March 2005
Accepted: 10 November 2005
Published online: 14 May 2007

MSC codes

  1. 68P05
  2. G8P10

Keywords

  1. binary search trees
  2. splay trees
  3. competitiveness

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